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Simplifying 2x2 + -13x = 1 Reorder the terms: -13x + 2x2 = 1 Solving -13x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -13x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -6.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -6.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -6.5x + x2 = 0 + 0.5 -6.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -6.5x + x2 = 0.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 0.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 0.5 + 10.5625 Combine like terms: 0.5 + 10.5625 = 11.0625 10.5625 + -6.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + -3.25) equal to 3.326033674 and -3.326033674.Subproblem 1
x + -3.25 = 3.326033674 Simplifying x + -3.25 = 3.326033674 Reorder the terms: -3.25 + x = 3.326033674 Solving -3.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 3.326033674 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.326033674 + 3.25 x = 3.326033674 + 3.25 Combine like terms: 3.326033674 + 3.25 = 6.576033674 x = 6.576033674 Simplifying x = 6.576033674Subproblem 2
x + -3.25 = -3.326033674 Simplifying x + -3.25 = -3.326033674 Reorder the terms: -3.25 + x = -3.326033674 Solving -3.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -3.326033674 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.326033674 + 3.25 x = -3.326033674 + 3.25 Combine like terms: -3.326033674 + 3.25 = -0.076033674 x = -0.076033674 Simplifying x = -0.076033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.576033674, -0.076033674}
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